A novel formulation of immersed boundary method incorporating a direct forcing approach within the SIMPLE method is presented for the simulation of incompressible flows. Both the incompressibility and the no-slip kinematic constraints are treated implicitly as distributed Lagrange multipliers and are fully coupled with each other by combining them into a single system of equations constituting the regularized saddle point problem. An intelligent and physically justified approximation of the system resembling the technique typical of the penalty method is carried out to facilitate the solution procedure. The approximated system is solved by utilizing the Schur complement approach, which allows using any available solver designed to simulate incompressible flows governed by the Helmholtz and Laplace operators and not originally enjoying the immersed boundary formalism. The capabilities of the developed methodology applied to the simulation of representative shear- and buoyancy-driven confined flows developing in the presence of stationary immersed bodies are demonstrated. A further application of the developed approach to moving boundary and two-way coupled fluid-structure interaction problems is discussed.